Pretty much like this screenshot. Just lock the party view to the bottom right (or any location tbh) instead of it being this wacky floating window. When you minimize it, simply have it lower below the screen so only the top bar shows, like a support chat on a website or something.

Also, add a LEAVE BUTTON and remove the X. It isn't clear that's a leave button.

TBH The party view and such should be as easy to use as possible and accessible from any screen. Open parties don't exist because the feature is a little weird to use. Global chat and party should be available on every screen because it's not clear that the global chat is even a thing because you only join it when you hit "multiplayer". 

There should also be a text chat for parties. Maybe have it so you can hit and F-key to open up the party menu? There's multiple options here, but general improvements to this could be helpful.edited:

EDIT:
Additional post, looks like public parties don't show up if you make them while in a game. You have to make it before you join a game. I don't think this is intended behavior. They also disappear when you "start" the game, which I think defeats the purpose entirely.

EDIT EDIT:
I just keep finding stuff with this entire system that doesn't work. Clicking the multiplayer menu while in a game basically doesn't work as intended. This entire menu just needs to be redone. It loads insanely slow and is basically useless it seems. It kind of works when not in a game sometimes.